docs: update TiDB Cloud links as vector search feature becomes public beta (#24667)

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docs/docs/integrations/memory/tidb_chat_message_history.ipynb

@@ -6,7 +6,7 @@
    "source": [
     "# TiDB\n",
     "\n",
-    "> [TiDB Cloud](https://tidbcloud.com/), is a comprehensive Database-as-a-Service (DBaaS) solution, that provides dedicated and serverless options. TiDB Serverless is now integrating a built-in vector search into the MySQL landscape. With this enhancement, you can seamlessly develop AI applications using TiDB Serverless without the need for a new database or additional technical stacks. Be among the first to experience it by joining the waitlist for the private beta at https://tidb.cloud/ai.\n",
+    "> [TiDB Cloud](https://pingcap.com/ai), is a comprehensive Database-as-a-Service (DBaaS) solution, that provides dedicated and serverless options. TiDB Serverless is now integrating a built-in vector search into the MySQL landscape. With this enhancement, you can seamlessly develop AI applications using TiDB Serverless without the need for a new database or additional technical stacks. Create a free TiDB Serverless cluster and start using the vector search feature today!\n",
     "\n",
     "This notebook introduces how to use TiDB to store chat message history. "
    ]

docs/docs/integrations/providers/tidb.mdx

@@ -1,10 +1,10 @@
 # TiDB
 
-> [TiDB Cloud](https://tidbcloud.com/), is a comprehensive Database-as-a-Service (DBaaS) solution, 
+> [TiDB Cloud](https://pingcap.com/ai), is a comprehensive Database-as-a-Service (DBaaS) solution,
 > that provides dedicated and serverless options. `TiDB Serverless` is now integrating 
 > a built-in vector search into the MySQL landscape. With this enhancement, you can seamlessly 
 > develop AI applications using `TiDB Serverless` without the need for a new database or additional 
-> technical stacks. Be among the first to experience it by joining the [waitlist for the private beta](https://tidb.cloud/ai).
+> technical stacks. Create a free TiDB Serverless cluster and start using the vector search feature today.
 
 
 ## Installation and Setup